A218360 Minimal order of degree-n irreducible polynomials over GF(13).

1, 7, 9, 5, 30941, 63, 5229043, 32, 27, 11, 23, 45, 53, 29, 4651, 64, 103, 19, 12865927, 25, 43, 161, 1381, 288, 701, 371, 81, 145, 1973, 31, 311, 128, 207, 721, 211, 37, 1481, 90061489, 79, 41, 6740847065723, 261, 119627, 115, 181, 47, 183959, 576, 1667, 101

Offset

1,2

Comments

a(n) < 13^n.

Links

Max Alekseyev, Table of n, a(n) for n = 1..416

Eric Weisstein's World of Mathematics, Irreducible Polynomial

Eric Weisstein's World of Mathematics, Polynomial Order

Formula

a(n) = min(M(n)) with M(n) = {d : d|(13^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A218337(n,1) = A213224(n,6).

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(13^n-1) minus U(n-1) end:
U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
a:= n-> min(M(n)[]):
seq(a(n), n=1..33);

Mathematica

M[n_] := M[n] = Divisors[13^n - 1]~Complement~U[n - 1];
U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
a[n_] := Min[M[n]];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A213224, A218337.

Sequence in context: A132715 A154910 A063603 * A020788 A198921 A099877

Adjacent sequences: A218357 A218358 A218359 * A218361 A218362 A218363

Keyword

nonn

Author

Alois P. Heinz, Oct 27 2012

Status

approved